Computational Methods and Production Engineering: Research and Development

By J. Paulo Davim

Computational Methods and Production Engineering: Research and Development is an original book publishing refereed, high quality articles with a special emphasis on research and development in production engineering and production organization for modern industry. Innovation and the relationship between computational methods and production engineering are presented.

Contents include: Finite Element method (FEM) modeling/simulation; Artificial neural networks (ANNs); Genetic algorithms; Evolutionary computation; Fuzzy logic; neuro-fuzzy systems; Particle swarm optimization (PSO); Tabu search and simulation annealing; and optimization techniques for complex systems.

As computational methods currently have several applications, including modeling manufacturing processes, monitoring and control, parameters optimization and computer-aided process planning, this book is an ideal resource for practitioners.

• Presents cutting-edge computational methods for production engineering
• Explores the relationship between applied computational methods and production engineering
• Presents new innovations in the field
• Edited by a key researcher in the field

• Language: English
• Publisher: Elsevier Science
• Release date: May 25, 2017
• ISBN: 9780857094827

Book preview

Computational Methods and Production Engineering

Research and Development

First Edition

J. Paulo Davim

University of Aveiro, Aveiro, Portugal

Table of Contents

Cover image

Title page

Copyright

List of contributors

About the editor

Preface

1: Parallel direct solver for finite element modeling of manufacturing processes

Abstract

Acknowledgments

1.1 Introduction

1.2 Brief review of standard gauss elimination

1.3 Structure of the parallel direct solver

1.4 Test cases and evaluation parameters

1.5 Results and discussion

1.6 Conclusions

Appendix

2: Optimal inspection/actuator placement for robust dimensional compensation in multistage manufacturing processes

Abstract

2.1 Introduction

2.2 State-space approach for modeling multistage assembly processes

2.3 Feed-forward predictive control

2.4 Optimal inspection/actuator placement for feed-forward control

2.5 Case study

2.6 Conclusions

Appendix

3: Numerical optimization strategies for springback compensation in sheet metal forming

Abstract

Acknowledgments

3.1 Introduction

3.2 Springback compensation strategies

3.3 Modeling strategies

3.4 Evaluation strategies

3.5 Optimization algorithms

3.6 Parameterization strategies

3.7 Case study: U-rail

3.8 Results and discussion

3.9 Conclusions

4: Finite element modeling of hot rolling: Steady- and unsteady-state analyses

Abstract

4.1 Introduction

4.2 Thermomechanical analysis of hot rolling: An overview

4.3 Work-roll and workpiece interface behavior

4.4 Constitutive equation for material model

4.5 Basic steps of FEM

4.6 Different approaches in FEM

4.7 Solution methods

4.8 Steady- and unsteady-state analyses of hot rolling

4.9 Concluding remarks

5: Numerical modeling methodologies for friction stir welding process

Abstract

5.1 Introduction to FSW

5.2 Modeling of FSW: Requirement and complexities

5.3 General steps for modeling a process

5.4 Modeling of FSW with Lagrangian analysis

5.5 Modeling of FSW with Eulerian analysis

5.6 Modeling of FSW with coupled Eulerian-Lagrangian (CEL) analysis

5.7 Comparison of modeling methods

5.8 Conclusion

6: Modeling of hard machining

Abstract

6.1 Introduction to hard machining

6.2 Numerical modeling of hard machining

6.3 Soft computing and statistical methods modeling of hard machining

6.4 Conclusions

7: Multiresponse optimization in wire electric discharge machining (WEDM) of HCHCr steel by integrating response surface methodology (RSM) with differential evolution (DE)

Abstract

7.1 Introduction

7.2 Experimental work

7.3 Response surface methodology

7.4 Results and discussion

7.5 Differential evolution (DE) optimization

7.6 Conclusions

Index

Copyright

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Notices

Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary.

Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility.

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List of contributors

J.V. Abellán-Nebot     Universitat Jaume I, Castelló de la Plana, Spain

A. Andrade-Campos     University of Aveiro, Aveiro, Portugal

E. Ferreira

University of Aveiro, Aveiro

University of Coimbra, Coimbra, Portugal

V.N. Gaitonde     B.V.B. College of Engineering and Technology, Hubli, India

Rahul Jain     Indian Institute of Technology, Kharagpur, India

N.E. Karkalos     National Technical University of Athens, Athens, Greece

S.R. Karnik     B.V.B. College of Engineering and Technology, Hubli, India

J. Liu     The University of Arizona, Tucson, AZ, United States

A. Maia     University of Aveiro, Aveiro, Portugal

M. Manjaiah     GeM Lab, Nantes, France

S. Maradi     B.V.B. College of Engineering and Technology, Hubli, India

A.P. Markopoulos     National Technical University of Athens, Athens, Greece

P.A.F. Martins     Universidade de Lisboa, Lisbon, Portugal

L.F. Menezes     University of Coimbra, Coimbra, Portugal

C.V. Nielsen     Technical University of Denmark, Lyngby, Denmark

M.C. Oliveira     University of Coimbra, Coimbra, Portugal

Surjya K. Pal     Indian Institute of Technology, Kharagpur, India

J. Paulo Davim     University of Aveiro, Aveiro, Portugal

I. Peñarrocha     Universitat Jaume I, Castelló de la Plana, Spain

P.M. Petkar     B.V.B. College of Engineering and Technology, Hubli, India

Matruprasad Rout     Indian Institute of Technology, Kharagpur, India

E. Sales-Setién     Universitat Jaume I, Castelló de la Plana, Spain

Shiv B. Singh     Indian Institute of Technology, Kharagpur, India

About the editor

J. Paulo Davim received his PhD in Mechanical Engineering in 1997, MSc degree in Mechanical Engineering (materials and manufacturing processes) in 1991, Dipl.-Ing Engineer’s degree (5 years) in Mechanical Engineering in 1986, from the University of Porto (FEUP), the Aggregate title (Full Habilitation) from the University of Coimbra in 2005 and a DSc from London Metropolitan University in 2013. He is Eur Ing by FEANI-Brussels and Senior Chartered Engineer by the Portuguese Institution of Engineers with a MBA and Specialist title in Engineering and Industrial Management. Currently, he is Professor at the Department of Mechanical Engineering of the University of Aveiro, Portugal. He has more than 30 years of teaching and research experience in Manufacturing, Materials, and Mechanical Engineering with special emphasis in Machining and Tribology. He has also interest in Management/Industrial Engineering and Higher Education for Sustainability/Engineering Education. He has received several scientific awards. He has worked as evaluator of projects for international research agencies as well as examiner of PhD thesis for many universities. He is the Editor in Chief of several international journals, Guest Editor of journals, books Editor, book Series Editor, and Scientific Advisory for many international journals and conferences. Presently, he is an Editorial Board member of 30 international journals and acts as reviewer for more than 80 prestigious Web of Science journals. In addition, he has also published as editor (and coeditor) of more than 100 books and as author (and coauthor) of more than 10 books, 80 book chapters, and 400 articles in journals and conferences (more than 200 articles in journals indexed in Web of Science/h-index 37+ and SCOPUS/h-index 45+).

J. Paulo Davim, University of Aveiro, Aveiro, Portugal

Preface

Production engineering is a branch of engineering that involves the design, development, implementation, operation, maintenance, and control of all processes in the manufacture of a product. It is an interdisciplinary subject requiring the collaboration of individuals trained in manufacturing engineering, industrial engineering, product design, management, etc.

Recently, there has been increased interest in developing computational methods to be applied in production engineering. Consequently, in production engineering, computational methods have achieved several applications, namely, modeling manufacturing processes, monitoring and control, parameters optimization and computer-aided process planning, etc.

This research book aims to provide information on computational methods and production engineering for modern industry. The initial chapter of the book provides parallel direct solver for finite element modeling of manufacturing processes. Chapter 2 is dedicated to optimal inspection/actuator placement for robust dimensional compensation in multistage manufacturing processes. Chapter 3 presents numerical optimization strategies for springback compensation in sheet metal forming. Chapter 4 covers finite element modeling of hot rolling (steady- and unsteady-state analyses). Chapter 5 is dedicated to numerical modeling methodologies for friction stir welding process. Chapter 6 contains information on modeling of hard machining. Finally, the last chapter of the book is dedicated to multiresponse optimization in wire electric discharge machining (WEDM) of HCHCR steel by integrating response surface methodology (RSM) with differential evolution (DE).

The present book can be used as a research book for final undergraduate engineering course or as a topic on computational methods and production engineering at the postgraduate level. This book can serve as reference for academics, researchers, manufacturing, mechanical and industrial engineers, as well as professionals in production engineering. Also, this book presents scientific interest for industry, centers of the research, laboratories, and universities throughout the world.

The editor acknowledges Woodhead/Elsevier for this opportunity and for their professional support. Finally, I would like to thank all the chapter authors for their availability for this work.

J. Paulo Davim, University of Aveiro, Aveiro, Portugal

1

Parallel direct solver for finite element modeling of manufacturing processes

C.V. Nielsen*; P.A.F. Martins†    * Technical University of Denmark, Lyngby, Denmark

† Universidade de Lisboa, Lisbon, Portugal

Abstract

This chapter describes and evaluates the parallelization of a direct equation solver for implementation in the finite element modeling of manufacturing processes. The parallel solver is implemented in an existing three-dimensional finite element computer program for problems including large deformations, contact development, and electrical and thermal fields. Speed-up and efficiency are evaluated on a standard personal computer. Considerable time savings are achieved, allowing computations to take place in industry within reasonable computation time without access to any kind of supercomputers or clusters. The direct equation solver is parallelized for shared memory platforms by OpenMP instructions, and it can be directly implemented in existing finite element codes utilizing skyline matrix storage, no matter the physical dimensions of the problems dealt with. Only the call to the existing solver has to be substituted by a call to the proposed parallel solver. The modification of the parallel direct equation solver to be applied as preconditioner of iterative equation solvers is also discussed. The FORTRAN source code is provided in the Appendix.

Keywords

Direct solver; Parallelization; OpenMP; FEM; Numerical methods

Acknowledgments

The authors would like to acknowledge the support provided by Fundação para a Ciência e a Tecnologia of Portugal and IDMEC under LAETA—UID/EMS/50022/2013 and PDTC/EMS-TEC/0626/2014.

1.1 Introduction

The central processing unit (CPU) time is of paramount importance in finite element modeling of manufacturing processes. Because the most significant part of the CPU time is consumed in solving the main system of equations resulting from finite element assemblies, different approaches have been developed to optimize solutions and reduce the overall computational costs of large finite element models.

The simplest approach is to apply faster solution techniques by replacing direct equation solvers by iterative equation solvers. There are various types of iterative solvers but the conjugate gradient (CG) iterative solvers proposed by Lanczos (1952) and Hestenes and Stiefel (1952) are among the simplest and more widely used in finite element computer programs.

Despite the advantages of CG iterative solvers, there are two major concerns (and challenges) related to its utilization in finite element modeling of manufacturing processes. First, precision is lost compared to that of direct solvers, because final accuracy depends on the threshold value utilized for accepting the solution, which inevitably results from a compromise between the desired accuracy and the required CPU time. In case small inaccuracies accumulate during finite element modeling of a manufacturing process involving a large number of solution steps, they may lead to poor satisfaction of the boundary conditions and to inaccuracies in fulfilling symmetry conditions. For instance, a zero displacement associated with a symmetry line (or plane) may be computed as a very small nonzero displacement creating problems in the overall final accuracy of the numerical simulation. In problems involving contact the earlier mentioned problems may, for larger threshold values, also disturb the contact algorithms, eventually leading to penetration in contact pairs.

The second drawback results from the fact that CG iterative solvers suffer from low robustness and applicability in case of ill-conditioned equation systems. In fact, iterative solvers have been reported unstable when dealing with ill-conditioned equation systems, whereas direct solvers have proved to be more robust (Farhat and Wilson, 1988). This is particularly relevant for finite element formulations that make use of penalties (i.e., very large numbers) to impose material incompressibility and/or to handle contact between different objects (e.g., deformable vs. deformable objects and/or deformable vs. rigid objects) and for simulations with large rigid body motion (e.g., when a preform is settling into a metal forming die undergoing very little deformation).

Among various improvements to optimize convergence and to improve the CPU time of CG iterative solvers, preconditioning and parallelization have been the most widely used techniques (Meijerink and van der Vorst, 1977).

A more complex approach to optimize solutions and reduce the overall computational cost of large finite element models has been achieved by decomposition of a finite element model into subdomains that are simultaneously solved by means of parallel computation (Kim and Im, 2003). The interface nodes between subdomains require communication between different processors and, therefore its overall number should be minimized in order to avoid computational bottlenecks. Farhat (1988) and Al-Nasra and Nguyen (1992) were among the first researchers to explore the trade-off between the number of interface nodes and subdomain size and to propose algorithms for optimal decompositions.

Parallelization of direct solvers is usually not considered as an alternative to parallelization of CG iterative solvers because it requires large amount of data communication between processors and also because it is considered more tedious and difficult to implement in existing finite element computer programs. However, parallelization of direct solvers may be an appropriate solution for two-dimensional finite element analysis of manufacturing processes, for three-dimensional analysis of manufacturing processes involving medium size models, and for preconditioning CG iterative solvers. In addition to what is mentioned earlier, it is worth noting that the solution accuracy of parallel direct solvers is identical to that of sequential direct solvers and that parallel direct solvers can also be utilized with solution decomposition approaches regardless of the problem to be solved.

Farhat and Wilson (1988) were among the first researchers to present parallel direct solvers. Parallelization can be applied for local memory processors as well as for shared memory processors, where the first is typically applied to a cluster of multiple computers, whereas the latter typically would be one computer with multiple threads.

Synn and Fulton (1995) were also among the first researchers to propose evaluation procedures to predict the performance of parallel direct solvers using skyline matrix storage. The usage of skyline or more efficient compressed sparse row storage formats is very often utilized in computer programs as it explores the large sparsity of the equation systems that are typical of finite element models in manufacturing.

In the present chapter a parallel direct solver for shared memory processors is presented and evaluated. The implementation is carried out in a personal computer (PC) due to increasing requirements from industry for running finite element simulations in standard hardware equipped with several cores and threads with shared memory. It is therefore an obvious request that the finite element computer programs can utilize multiple threads to reduce the computation time.

The direct solver to be presented is parallelized by OpenMP instructions in a FORTRAN implementation. The structure of the solver is explained in the chapter, and its performance is evaluated in terms of speed-up and efficiency. Amdahl's law (Hill and Marty, 2008) is applied to evaluate the amount of the code being parallel and to evaluate the potential benefit associated with an increasing number of threads. The entire source code is provided in the Appendix for the benefit of those who develop finite element computer programs. Only the call to the solver in existing computer programs using the same matrix storage format has to be replaced by a call to the presented solver. The requested inputs are the stiffness matrix in appropriate storage format together with the corresponding pointers to the diagonal positions, the right-hand side, the number of equations, and the number of threads to be utilized. A special implementation of the parallel direct solver that can be effectively and efficiently utilized as a preconditioner of parallel CG iterative solvers is also discussed.

A benchmark test case and a resistance spot welding test case selected from an industrial application enrich the overall presentation. The industrial example requires solution of a coupled electro-thermo-mechanical model in three dimensions with contact between individual hexahedral meshes. The case is further complicated by having large temperature gradients across the contacting interfaces, and therefore also large gradients in the mechanical stress response.

1.2 Brief review of standard gauss elimination

1.2.1 Skyline matrix storage

The presentation of the parallel direct solver is focused on the equation systems resulting from typical finite element assemblies,

   (1.1)

where [Amatrix and {x} and {bvectors containing the unknowns and the right-hand side, respectively.

Due to symmetry of the system matrix, only half of the matrix needs to be built and stored (slightly more than half due to storage of all diagonal positions). Furthermore, since most finite element equation systems are sparse and by proper node numbering have many zeros far from the diagonal, it is common to employ skyline storage to reduce memory requirements by omitting all zeros above the highest skyline positions (Fig. 1.1). Zeros may still exist below this envelope as the skyline encloses all nonzero positions.

Fig. 1.1 System matrix storage by utilizing symmetry (left) and skyline format by omitting zeros (right). Only the grayed positions are stored. The dashed line covering the highest skyline positions indicates the requirements in case of banded matrix storage format.

In skyline matrix storage, the equation system is typically stored in a one-dimensional vector {s} with an additional index vector {i} pointing to the diagonal positions. This is illustrated in Fig. 1.2 up to the 7th column. The size of the skyline vector will be the number of positions under the skyline. The size of the index vector equals the number of rows or columns n. Then, it follows that the size of the skyline vector is in as the last diagonal is the last position in the skyline vector.

Fig. 1.2 Format of skyline vector { s } and index vector { i } based on the original system matrix [ A ]. Numbers correspond to the position in the skyline vector.

1.2.2 Gauss elimination

Among various solution techniques used by direct solvers, Gauss elimination was chosen due to its wide utilization and adequacy for parallelization. The solution of an equation system by Gauss elimination with column reduction comprises the following three basic steps:

• factorization of the system matrix and reduction of the right-hand side vector (this step is performed column by column, thereby being with column reduction)

• division of the right-hand side vector by the diagonals of the system matrix

• backward substitution.

1.2.2.1 Factorization of the system matrix and reduction of the right-hand side vector

The first step in the factorization of the system matrix is illustrated by Fig. 1.3A for column j have been processed. The number of operations equals the active column height −2 as the diagonal position and the topmost position are not processed. The illustration in Fig. 1.3A has active column height 7 and five operations are depicted in the subfigures. In each operation, the kth position is subtracted from the dot product formed by the vectors marked by os and xs, i.e.

Fig. 1.3 Factorization of system matrix and reduction of right-hand side. (A) Reduction of off-diagonal positions in column j by subtraction of dot product formed by os and xs. (B) Reduction of diagonal positions in system matrix and reduction of right-hand side vector.

   (1.2)

Hereafter, all positions above the diagonal are divided by the diagonal position in the same row. In Fig. 1.3B, this corresponds to

   (1.3)

where division is position-wise. This is followed by reduction of the diagonal term by

   (1.4)

which means subtraction of each multiplication of new and old off-diagonal position. New is defined as "after Eq. (1.3) and old is defined as before Eq. (1.3)."

Finally, the jth position in the right-hand side vector is reduced by subtraction of the dot product spanned by the marked xs and vs in Fig. 1.3B. Note that the positions marked by xs are now the latest updated, meaning after (1.4). The reduction of the right-hand side vector can be written as

   (1.5)

1.2.2.2 Division of right-hand side vector by system matrix diagonals

This step is straight forward: Each position, j, in the right-hand side vector is divided by the system matrix diagonal term from the jare eliminated from the jth row.

1.2.2.3 Backward substitution

The unknowns are now found by backward substitution and stored in the right-hand side vector {b}. The right-hand side vector is processed backward, such that Fig. 1.4 illustrates the substitution for the jalready processed. The positions marked by vs in the figure are modified by subtraction of positions in the system matrix marked by xs in the jth column. Before subtraction, these positions are multiplied by bj, the jth position in the right-hand side vector, that is

Fig. 1.4 in right-hand side vector by subtraction of system matrix positions marked by xs multiplied by the j th position of the right-hand side vector.

   (1.6)

.

1.3 Structure of the parallel direct solver

The parallelization of the direct solver with skyline matrix storage is explained in this section with variable names matching the source code included in the Appendix. The factorization of the system matrix and reduction of the right-hand side (Section 1.2.2.1) is parallelized, whereas the division of the right-hand side vector by the system matrix diagonals (Section 1.2.2.2) as well as the backward substitution (Section 1.2.2.3) is left sequential as the time spent on these tasks is marginal compared to the factorization and reduction. The remaining of this section is devoted to the description of the parallelized part of the solver.

A few variables are introduced preliminary:

1.3.1 Parallel region

The factorization and reduction are performed within a parallel region defined by